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searching for Measure space 58 found (195 total)

Σ-algebra (5,337 words) [view diff] exact match in snippet view article find links to article

generated (since its cardinality is higher than continuum). A separable measure space has a natural pseudometric that renders it separable as a pseudometric

Modes of convergence (928 words) [view diff] no match in snippet view article find links to article

In mathematics, there are many senses in which a sequence or a series is said to be convergent. This article describes various modes (senses or species)

Modes of convergence (annotated index) (865 words) [view diff] exact match in snippet view article

⇒ {\displaystyle \Rightarrow } convergence in measure. (In a finite measure space) - Almost uniform convergence ⇒ {\displaystyle \Rightarrow } convergence

Filtration (probability theory) (730 words) [view diff] exact match in snippet view article

, P ) {\displaystyle (\Omega ,{\mathcal {F}}_{i},P)} is a complete measure space for every i ∈ I . {\displaystyle i\in I.} (The converse is not necessarily

Permutational analysis of variance (604 words) [view diff] exact match in snippet view article find links to article

hypothesis that the centroids and dispersion of the groups as defined by measure space are equivalent for all groups. A rejection of the null hypothesis means

Poisson boundary (2,285 words) [view diff] exact match in snippet view article find links to article

In mathematics, the Poisson boundary is a measure space associated to a random walk. It is an object designed to encode the asymptotic behaviour of the

Non-commutative conditional expectation (490 words) [view diff] exact match in snippet view article find links to article

bounded measurable functions on a σ {\displaystyle \sigma } -finite measure space ( X , μ ) {\displaystyle (X,\mu )} is the canonical example of a commutative

Probability measure (970 words) [view diff] exact match in snippet view article find links to article

although the fundamental concept of a system in statistical mechanics is a measure space, such measures are not always probability measures. In general, in statistical

Hilbert–Schmidt operator (1,391 words) [view diff] exact match in snippet view article find links to article

where ( X , Ω , μ ) {\displaystyle \left(X,\Omega ,\mu \right)} is a measure space, then the integral operator K : L 2 ( μ ) → L 2 ( μ ) {\displaystyle

Separable space (2,071 words) [view diff] exact match in snippet view article find links to article

spaces L p ( X , μ ) {\displaystyle L^{p}\left(X,\mu \right)} , over a measure space ⟨ X , M , μ ⟩ {\displaystyle \left\langle X,{\mathcal {M}},\mu \right\rangle

Doubling space (911 words) [view diff] exact match in snippet view article find links to article

be proved that, necessarily, C ≥ {\displaystyle \geq } 2. A metric measure space that supports a doubling measure is necessarily a doubling metric space

Conull set (153 words) [view diff] exact match in snippet view article find links to article

Führ, p. 143. Bezuglyi, Sergey (2000), "Groups of automorphisms of a measure space and weak equivalence of cocycles", Descriptive set theory and dynamical

Nepal PQ-1 (308 words) [view diff] exact match in snippet view article find links to article

and developed with readily available commercial components (COTS) to measure space radiation while orbiting, and periodically transmit it to Earth. The

Commutation theorem for traces (2,664 words) [view diff] exact match in snippet view article find links to article

\ell ^{2}(\Gamma ),} a tensor product of Hilbert spaces. The group–measure space construction or crossed product von Neumann algebra M = A ⋊ Γ {\displaystyle

OV1-11 (921 words) [view diff] exact match in snippet view article find links to article

measure UV radiance. Two spectrometers and a faraday cup were designed to measure space plasmas. Another experiment would measure the oxygen in the upper atmosphere

Ba space (872 words) [view diff] exact match in snippet view article find links to article

absolutely continuous with respect to μ (μ-a.c. for short). When the measure space is furthermore sigma-finite then L∞(μ) is in turn dual to L1(μ), which

Dual norm (2,937 words) [view diff] exact match in snippet view article find links to article

norms, where ( X , Σ , μ ) , {\displaystyle (X,\Sigma ,\mu ),} is some measure space. In particular the Euclidean norm is self-dual since p = q = 2. {\displaystyle

Wiener–Wintner theorem (234 words) [view diff] exact match in snippet view article find links to article

Wintner (1941). Suppose that τ is a measure-preserving transformation of a measure space S with finite measure. If f is a real-valued integrable function on

Etruscan religion (3,155 words) [view diff] exact match in snippet view article find links to article

ways to found cities, erect shrines, drain fields, formulate laws, and measure space and time. The Etrusca Disciplina was mainly a set of rules for the conduct

Conservative system (1,808 words) [view diff] exact match in snippet view article find links to article

countable union of wandering sets. The Hopf decomposition states that every measure space with a non-singular transformation can be decomposed into an invariant

Lusin's theorem (713 words) [view diff] exact match in snippet view article find links to article

measurable. Let ( X , Σ , μ ) {\displaystyle (X,\Sigma ,\mu )} be a Radon measure space and Y be a second-countable topological space equipped with a Borel

Metric space (11,073 words) [view diff] exact match in snippet view article find links to article

and a metric which are compatible with each other. Formally, a metric measure space is a metric space equipped with a Borel regular measure such that every

Wolfgang Krieger (485 words) [view diff] exact match in snippet view article find links to article

the ICM in Vancouver in 1974. On non-singular transformations of a measure space. I, Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete

Geography (9,361 words) [view diff] exact match in snippet view article find links to article

depending on the scale used. Scale is the frame that geographers use to measure space, and ultimately to try and understand a place. During the quantitative

Norm (mathematics) (5,671 words) [view diff] exact match in snippet view article

space L 2 ( X , μ ) {\displaystyle L^{2}(X,\mu )} associated with a measure space ( X , Σ , μ ) , {\displaystyle (X,\Sigma ,\mu ),} which consists of

Hellinger distance (1,780 words) [view diff] exact match in snippet view article find links to article

{\displaystyle P} and Q {\displaystyle Q} denote two probability measures on a measure space X {\displaystyle {\mathcal {X}}} that are absolutely continuous with

Negligible set (708 words) [view diff] exact match in snippet view article find links to article

directed sets, you get the same result, but for nets.) Or, let X be a measure space, and let negligible sets be the null sets. If Y is the real line R,

Semi-continuity (2,561 words) [view diff] exact match in snippet view article find links to article

{\displaystyle {\sqrt {2}}} . Let ( X , μ ) {\displaystyle (X,\mu )} be a measure space and let L + ( X , μ ) {\displaystyle L^{+}(X,\mu )} denote the set of

Asymptotic equipartition property (3,951 words) [view diff] exact match in snippet view article find links to article

P N = P × ⋯ × P {\displaystyle P^{N}=P\times \cdots \times P} of a measure space P, this sequence admits an asymptotically equivalent sequence HN of

Simple function (817 words) [view diff] exact match in snippet view article find links to article

{\displaystyle f} be a non-negative measurable function defined over the measure space ( X , Σ , μ ) {\displaystyle (X,\Sigma ,\mu )} . For each n ∈ N {\displaystyle

Hyperfinite type II factor (499 words) [view diff] exact match in snippet view article find links to article

factor. The hyperfinite type II1 factor also arises from the group-measure space construction for ergodic free measure-preserving actions of countable

Mixing (mathematics) (4,673 words) [view diff] exact match in snippet view article

some R n {\displaystyle \mathbb {R} ^{n}} , and so it is a Lebesgue measure space. Verifying strong-mixing can be simplified if we only need to check

Entropy (information theory) (9,715 words) [view diff] exact match in snippet view article

non-negative, and zero if p = m as measures. It is defined for any measure space, hence coordinate independent and invariant under co-ordinate reparameterizations

Mercer's theorem (1,783 words) [view diff] exact match in snippet view article find links to article

representations of measurable kernels. Let (X, M, μ) be a σ-finite measure space. An L2 (or square-integrable) kernel on X is a function K ∈ L μ ⊗ μ

Poincaré inequality (2,103 words) [view diff] exact match in snippet view article find links to article

Poincaré inequality is slightly different. One definition is: a metric measure space supports a (q,p)-Poincare inequality for some 1 ≤ q , p < ∞ {\displaystyle

Markov kernel (2,074 words) [view diff] exact match in snippet view article find links to article

X} a ( S , Y ) {\displaystyle (S,Y)} -valued random variable on the measure space ( Ω , F , P ) {\displaystyle (\Omega ,{\mathcal {F}},P)} and G ⊆ F {\displaystyle

Complemented subspace (3,308 words) [view diff] exact match in snippet view article find links to article

{\displaystyle M\oplus N} to X {\displaystyle X} . If Y {\displaystyle Y} is a measure space and X ⊆ Y {\displaystyle X\subseteq Y} has positive measure, then L

Projective tensor product (2,503 words) [view diff] exact match in snippet view article find links to article

Y\right).} For ( X , A , μ ) {\displaystyle (X,{\mathcal {A}},\mu )} a measure space, let L 1 {\displaystyle L^{1}} be the real Lebesgue space L 1 ( μ )

Følner sequence (924 words) [view diff] exact match in snippet view article find links to article

i} gets large. In the setting of a locally compact group acting on a measure space ( X , μ ) {\displaystyle (X,\mu )} there is a more general definition

Amenable group (3,135 words) [view diff] exact match in snippet view article find links to article

space L∞(G) of essentially bounded measurable functions within this measure space (which is clearly independent of the scale of the Haar measure). Definition

Donald John Roberts (648 words) [view diff] exact match in snippet view article find links to article

selection Roberts, Donald John. "Existence of Lindahl equilibrium with a measure space of consumers." Journal of Economic Theory 6.4 (1973): 355-381. Champsaur

Singular value decomposition (13,747 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \mathbf {U} ,} a unitary V , {\displaystyle \mathbf {V} ,} a measure space ( X , μ ) , {\displaystyle (X,\mu ),} and a non-negative measurable

Ergodicity (8,819 words) [view diff] exact match in snippet view article find links to article

shift-invariant measures. A transformation T {\displaystyle T} of a probability measure space ( X , μ ) {\displaystyle (X,\mu )} is said to be mixing for the measure

Equidistributed sequence (2,394 words) [view diff] exact match in snippet view article find links to article

well-distributed modulo 1 is analogous. For an arbitrary probability measure space ( X , μ ) {\displaystyle (X,\mu )} , a sequence of points ( x n ) {\displaystyle

Interpolation space (5,335 words) [view diff] exact match in snippet view article find links to article

behaves well under complex interpolation. If (R, Σ, μ) is an arbitrary measure space, if 1 ≤ p0, p1 ≤ ∞ and 0 < θ < 1, then ( L p 0 ( R , Σ , μ ) , L p 1

Generative adversarial network (14,084 words) [view diff] no match in snippet view article find links to article

set of all probability measures μ G {\displaystyle \mu _{G}} on the measure-space ( Ω , B ) {\displaystyle (\Omega ,{\mathcal {B}})} . The discriminator's

Field of sets (3,670 words) [view diff] exact match in snippet view article find links to article

(which may be called abstract sigma algebras) and measurable spaces. A measure space is a triple ( X , F , μ ) {\displaystyle (X,{\mathcal {F}},\mu )} where

Stefaan Vaes (419 words) [view diff] exact match in snippet view article find links to article

requires |journal= (help) Popa, Sorin; Vaes, Stefaan (2009). "Group measure space decomposition of II1 factors and W*-superrigidity". Inventiones Mathematicae

Information theory and measure theory (1,754 words) [view diff] exact match in snippet view article find links to article

measure. Thinking of both the integral and the sum as integration on a measure space allows for a unified treatment. Consider the formula for the differential

Schwinger function (2,553 words) [view diff] exact match in snippet view article find links to article

Ergodicity. The time translation semigroup acts ergodically on the measure space ( D ′ ( R d ) , d μ ) {\displaystyle (D'(\mathbb {R} ^{d}),d\mu )}

Direct integral (2,820 words) [view diff] exact match in snippet view article find links to article

corresponding to any central decomposition of W*(π) over a standard measure space (X, μ) (which, as stated, is unique in a measure theoretic sense), there

Standard probability space (4,350 words) [view diff] exact match in snippet view article find links to article

it)). "There is a coherent way to ignore the sets of measure 0 in a measure space" (Petersen 1983, page 15). Striving to get rid of null sets, mathematicians

Schuette–Nesbitt formula (2,873 words) [view diff] exact match in snippet view article find links to article

probabilistic versions (4'), (5') and (6') can be generalized to every finite measure space. For textbook presentations of the probabilistic Schuette–Nesbitt formula

Science of Logic (13,120 words) [view diff] exact match in snippet view article find links to article

only an intellectual abstraction, though, since it merely serves to measure space by the Rule of time or time by the Rule of space. It supplies no objective

2015 in science (23,993 words) [view diff] exact match in snippet view article find links to article

Retrieved 9 January 2015. "Astronomers use vanishing neutron star to measure space-time warp". Science Daily. 8 January 2015. Retrieved 10 January 2015

List of fellows of IEEE Dielectrics & Electrical Insulation Society (57 words) [view diff] exact match in snippet view article find links to article

Tatsuo Takada "For contributions to the development of technology to measure space charge in solid and liquid dielectric materials" 1999 Arthur Yelon "For

Rokhlin lemma (3,893 words) [view diff] exact match in snippet view article find links to article

roles in their respective fields are fundamental. A Lebesgue space is a measure space ( X , B , μ ) {\displaystyle (X,{\mathcal {B}},\mu )} composed of two

Monotone comparative statics (8,478 words) [view diff] exact match in snippet view article find links to article

Let ( T , T , μ ) {\displaystyle (T,{\mathcal {T}},\mu )} be a finite measure space and suppose that, for each s ∈ S {\displaystyle s\in S} , f ( s ; t